Is the prayer valid despite the continuous emission of gases – with certainty, not merely a delusion – due to an organic disease, given that it cannot be controlled and affects the timely performance of prayers?

If the wind (gas) exits sometimes and stops at other times, and the duration of its cessation is long at times and short at others, and it precedes sometimes and delays at others, then your ruling is the same as that of a person afflicted with سلس (incontinence). You should perform ablution (wudu') for prayer after its time has begun, and pray the obligatory prayer and as many supererogatory prayers as you wish with this ablution.

However, if you know at any time that you can pray with a sound purification, then wait until you perform ablution and pray without anything exiting.